Wideband modeling of linear electrical components (such as devices and systems) from measured data is of growing importance for the design and verification of electrical systems. The modeling is usually based on “fitting” a linear model by varying a set of parameters that characterize the model behavior, such as admittance (y), impedance (z), and scattering (s) parameters in the frequency domain or the time domain. The model can be based on a ratio of polynomials (see [1] E. C. Levy, “Complex curve fitting”, IRE Trans. Automatic Control, vol. 4, pp. 37-44, May 1959, [2] C. K. Sanathanan and J. Koerner, “Transfer function synthesis as a ratio of two complex polynomials”, IEEE Trans. Automatic Control, vol. 8, pp. 56-58, 1963), or orthogonal polynomial functions (see [3] C. P. Coelho, J. R. Phillips, and L. M. Silveira, “Generating high-accuracy simulation models using problem-tailored orthogonal polynomials basis”, IEEE Trans. Circuits and Systems-I, vol. 53, no. 12, pp. 2705-2714, December 2006). Recently, the pole relocating vector fitting technique (see [4] B. Gustaysen, and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting”, IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, July 1999) has become widely applied, and several enhancements have been proposed (see [5] S. Grivet-Talocia, “Package macromodeling via timedomain vector fitting”, IEEE Microwave and Wireless Components Letters, vol. 13, no. 11, pp. 472-474, November 2003, [6] B. Gustaysen, “Improving the pole relocating properties of vector fitting”, IEEE Trans. Power Delivery, vol. 21, no. 3, pp. 1587-1592, July 2006). The modeling is complete when the parameters have been found that describe the tabulated data with a given accuracy level. The fitting described in the literature is based on fitting the individual elements of the admittance matrix. The resulting model is therefore well suited for calculating the currents if the applied voltages are given.
However, there is no guarantee that the model will behave satisfactorily with a different terminal condition. For instance, the fit may be poor for the case that currents are given, and the voltages have to be determined. Such effects can occur in cases where the admittance matrix contains a large eigenvalue spread, such that the ratio between the largest and smallest eigenvalue is relatively large.